Some preliminary discussion is presented concerning predicting superconductivity in general and the properties of existing fullerene superconductors. This is followed by a consideration of the likelihood of superconductivity inC36solids. Our present knowledge aboutC36and the similar moleculeC24N12is reviewed along with the relevant arguments used as a basis for suggesting that these systems are good candidates for superconductivity at relatively high temperatures. ©1999 American Institute of Physics.